Homography apply

homography-apply · version 1.0.0 · Geometry, location & color · free, no key needed

Apply an exact 2D homography to a homogeneous point or line, including points at infinity.

Use when you need to: apply homography to point · transform homogeneous line · map point at infinity.

Decide before calling

Read the versioned contract and the supported scope below. Reuse homography-apply@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use homography-apply@1.0.0 for apply homography to point. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• apply homography to point
• transform homogeneous line
• map point at infinity
• exact projective coordinate transform
• apply planar perspective map
• transform 2D projective entity

Not supported

• raster image resampling
• geographic coordinate conversion

Behavior

• Canonical rationals are integers or reduced p/q strings with a positive denominator.
• Homogeneous outputs are primitive integer tuples with first nonzero coordinate positive.
• All arithmetic and predicates use exact BigInt cross-products; binary floating point and epsilon comparisons are never used.
• Reference: Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2.

Input

• matrix (array of array of string, required): min items 3; max items 3; each min items 3; each max items 3; each each min length 1; each each max length 256; each each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• kind (one of "point", "line", required)
• coordinates (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$

Output

• kind (one of "point", "line", required)
• coordinates (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• classification (one of "finite", "infinity", "line", required)
• reference (constant "Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2", required)

Limits

• max input bytes: 8192
• max rational bytes: 256
• max output bytes: 8192
• max tree nodes: 128

Example

Request input:

{
  "matrix": [
    [
      "1",
      "0",
      "0"
    ],
    [
      "0",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "1"
    ]
  ],
  "kind": "point",
  "coordinates": [
    "2",
    "3",
    "1"
  ]
}

Response:

{
  "result": {
    "kind": "point",
    "coordinates": [
      "2",
      "3",
      "1"
    ],
    "classification": "finite",
    "reference": "Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "homography-apply",
  "version": "1.0.0",
  "input": {
    "matrix": [
      [
        "1",
        "0",
        "0"
      ],
      [
        "0",
        "1",
        "0"
      ],
      [
        "0",
        "0",
        "1"
      ]
    ],
    "kind": "point",
    "coordinates": [
      "2",
      "3",
      "1"
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/homography-apply/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"matrix":[["1","0","0"],["0","1","0"],["0","0","1"]],"kind":"point","coordinates":["2","3","1"]}'

The machine-readable contract is at /v1/tools/homography-apply/versions/1.0.0.

CLI

node cli.mjs run homography-apply 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Affine2d apply: Apply one exact rational 2D affine map to bounded points or free vectors.
• Homography invert: Invert an exact nonsingular 2D homography and return a canonical projective matrix.
• Affine2d fixed set: Classify and compute the exact fixed locus of a rational 2D affine map.
• Homography compose: Compose two exact 2D homographies and return a canonical projective matrix.
• Homography incidence verify: Verify exact point-line incidence before and after a 2D homography with certificates.
• Affine2d compose: Compose two exact rational 2D affine maps in first-then-second order.